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It took me a lot of sitting with my megaminx with a lot of confused turning to figure out. I'll try explain in a way that made sense to me.

For faces other than U or D, you can observe that the effect of a a single one fifth turn on the two corners in the U/D layer is the same as a quarter turn on a 3x3. Since the inverse of a turn must undo the effect, we can say the same for the two corners brought into U/D by that turn. That leaves the one corner on the "equator zig-zag" (don't know what else to call it) as an unknown. Since the total corner twist on the entire puzzle must be a multiple of 3, you can work out that the orientation of the last corner can't be changed with a single fifth turn.

With edge orientation, it's a little trickier. A face turn must flip an even number of edges, but since there are 5 edges per face, at least one edge must keep it's orientation. On a 3x3 orientation is specified relative to an axis that is defined by the line passing through the F and B centres. On a megaminx, you can define a similar axis that doesn't pass through centres, but passes through two corners. It's easiest to explain with colours, I think. Assuming you have a megaminx with the default colour scheme, and hold white on top, green on front. Then the axis for orientation goes from the front-most corner (green-turquoise-pale yellow) to the back-most corner (blue-yellow-light green). Then the following rules for figuring out edge orientation apply:

Turning a face that does not contain the axis corner does not affect edge orientation.

Turning a face that contains an axis corner flips 4 edges. The edge that is not flipped is the edge that is between the corner that moves out of the axis position and the corner that moves into the axis position. Or, the edge that stays on the equator zig-zag does not change orientation.

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Then the axis for orientation goes from the front-most corner (green-turquoise-pale yellow) to the back-most corner (blue-yellow-light green). Then the following rules for figuring out edge orientation apply:

Turning a face that does not contain the axis corner does not affect edge orientation.

Turning a face that contains an axis corner flips 4 edges. The edge that is not flipped is the edge that is between the corner that moves out of the axis position and the corner that moves into the axis position. Or, the edge that stays on the equator zig-zag does not change orientation.

I don't think this leads to a consistent definition of EO for all 12 face turns. Let's say we set up our megaminx with DFL DFR' DFL' DFR2 F' DFR' F and ignore the corners. This is a 3-cycle of edges around the frontmost corner. If we perform an F move, then the F-DFR edge moves to the F-DFL position and is flipped, so the F-DFR edge must originally have been misoriented since it stays on the equatorial zig-zag. By symmetry, this also applies to the DFR and DFL moves, which means that all three edges in this 3-cycle are flipped, but that violates EO parity.

Looking at it again, you're right. I've came up with it about a year ago as part of an idea for an ZZ like approach to megaminx S2L (a terrible idea). Looking at it again now, I think I was on the wrong track trying to make it consistent with the common 3x3 definition of EO. Of course that doesn't matter at all for ksolve's purposes.

I know about the cube explorer's way of defining EO, but I just never thought of applying it to megaminx.

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When I had a look at mega EO, I found that the only way get consistent EO is by using a ring of an even number of faces otherwise you can send an edge around the ring and you will get the edges the other way up.

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So I was trying to generate a 2x2x Leg-1 and it doesn't work I don't know why. I' using this: https://www.cubing.net/ksolve.js/ I used this scramble code or what its called:
Scramble Leg-T4
CORNERS
1 2 3 4 5 7 6
0 0 1 1 1 1 1
End

ScrambleAlg Leg-T4
R' U' R U' F R2 F' R F R' F' D'
End

So why it doesn't work? Maybe the orientation vectors are wrong or something?

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